$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 4x - 3$ and $ BC = 9x - 43$ Find $AC$.
A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {4x - 3} = {9x - 43}$ Solve for $x$ $ -5x = -40$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 4({8}) - 3$ $ BC = 9({8}) - 43$ $ AB = 32 - 3$ $ BC = 72 - 43$ $ AB = 29$ $ BC = 29$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {29} + {29}$ $ AC = 58$